\[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
Test:
_divideComplex, real part
Bits:
128 bits
Bits error versus x.re
Bits error versus x.im
Bits error versus y.re
Bits error versus y.im
Time: 9.3 s
Input Error: 25.5
Output Error: 25.6
Log: ⚲
Profile: 🕒
\(\frac{1}{\frac{{y.re}^2 + y.im \cdot y.im}{y.re \cdot x.re + x.im \cdot y.im}}\)
  1. Started with
    \[\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}\]
    25.5
  2. Using strategy rm
    25.5
  3. Applied clear-num to get
    \[\color{red}{\frac{x.re \cdot y.re + x.im \cdot y.im}{y.re \cdot y.re + y.im \cdot y.im}} \leadsto \color{blue}{\frac{1}{\frac{y.re \cdot y.re + y.im \cdot y.im}{x.re \cdot y.re + x.im \cdot y.im}}}\]
    25.6
  4. Applied simplify to get
    \[\frac{1}{\color{red}{\frac{y.re \cdot y.re + y.im \cdot y.im}{x.re \cdot y.re + x.im \cdot y.im}}} \leadsto \frac{1}{\color{blue}{\frac{{y.re}^2 + y.im \cdot y.im}{y.re \cdot x.re + x.im \cdot y.im}}}\]
    25.6

Original test:


(lambda ((x.re default) (x.im default) (y.re default) (y.im default))
  #:name "_divideComplex, real part"
  (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))